Simplify. Rewrite the expression in the form $5^n$. $5^2\cdot 5^5=$
Explanation: $\begin{aligned} 5^2\cdot 5^5&=5^{2+5} \\\\ &=5^7 \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} 5^2\cdot 5^5&=\underbrace{5\cdot 5}_\text{2 times}\cdot\underbrace{5\cdot 5\cdot 5\cdot 5\cdot 5}_\text{5 times} \\\\\\ &=\underbrace{5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5}_\text{7 times} \\\\ &=5^7 \end{aligned}$ In conclusion, $5^2\cdot 5^5=5^7$.